# From Hazard Functions to Language Space: Cox-Supervised Distillation of Survival Risk into a Large Language Model

arXiv: https://arxiv.org/abs/2606.08945 · HTML: https://mlsanity.com/paper/2606.08945/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 44 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Builds on (most cited first, 10 of 10)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Datasets: A Community Library for Natural Language Processing](https://mlsanity.com/paper/2109.02846/) (2021)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [TabLLM: Few-shot Classification of Tabular Data with Large Language Models](https://mlsanity.com/paper/2210.10723/) (2022)
- [CK4Gen: A Knowledge Distillation Framework for Generating High-Utility Synthetic Survival Datasets in Healthcare](https://mlsanity.com/paper/2410.16872/) (2024)

## Abstract (arXiv)

We investigate whether information about time-to-event risk estimated by a Cox proportional hazards model can be transferred into a generative large language model. We propose a text-based survival modelling pipeline in which structured clinical covariates are converted into text prompts and a Qwen-based large language model is fine-tuned to generate patient-specific survival risk using Cox model predictions as a training target. Across GBSG2, ACTG320, and WHAS500, the model achieves competitive held-out discrimination and calibration despite being trained as a text-generation task rather than with a conventional survival-analysis loss. We further analyse the geometry of the model's hidden states, where t-SNE visualisations reveal smooth risk gradients in latent space, suggesting that the model represents survival risk as a continuous structure rather than isolated risk categories. Together, these findings suggest that large language models can internalise survival-risk structure while supporting calibrated prediction, providing a route towards time-to-event reasoning in language models.